Microwave Filters for Communication Systems: Fundamentals, Design and Applications

CHAPTER 4

COMPUTER-AIDED SYNTHESIS OF CHARACTERISTIC POLYNOMIALS

A lowpass prototype filter can be completely characterized in terms of its critical frequencies, the poles and zeros of the transfer function. This easily leads to the possibility of generating such critical frequencies for a desired response shape by adopting computer-aided optimization techniques. For most types of practical filters, analytic techniques already exist to compute the critical frequencies. However, such techniques are restricted to the well-defined filter functions such as the equiripple Chebyshev and elliptic functions, or the monotonically increasing maximally flat function. Any departure from these techniques necessitates a computer-aided optimization procedure.

This chapter is devoted to the synthesis of the characteristic polynomials of lowpass lossless prototype filters using an efficient computer-aided optimization technique. It includes minimum phase as well as linear phase filters exhibiting symmetric or asymmetric response. The technique is completely general and can be readily adapted to synthesize characteristic polynomials with an arbitrary response. Classical filters such as Chebyshev or elliptic function filters can be derived as special cases of the more general characteristic polynomials.

4.1 OBJECTIVE FUNCTION AND CONSTRAINTS FOR SYMMETRIC LOWPASS PROTOTYPE FILTER NETWORKS

The transmission coefficient of a symmetric minimum phase lowpass prototype filter network is given by (Section ...